1. Field of the Invention
The present invention relates to an apparatus and a method for simulating an electric current flowing through an electronic appliances by solving simultaneous linear equations defined depending on an analytic frequency, and to a program storage medium storing a program for realizing the simulation apparatus, and more specifically to a simulation apparatus and method for quickly realizing the simulating process, and a program storage medium storing a program used to realizing the simulation apparatus.
There is a social rule that excess electric waves or noise higher than a predetermined level should not be discharged. Actually, they have been strictly regulated according to individual rules in each country in the world.
To satisfy such regulations on electric waves, various countermeasures such as shielding technology, filtering technology, etc. are used. However, it is necessary to develop an appropriate simulating technology to quantitatively figure out to what extent electric waves can be attenuated by each of the technologies.
With the above described background, the Applicant of the present invention has disclosed the invention of a simulating technology to compute the intensity of an electromagnetic field discharged from an electronic appliances in the moment method. To put the simulating technology for practical use, a technology of performing a high-speed simulating process should be established.
2. Description of the Related Art
A method of simulating electromagnetic field analysis can be the difference method, the finite element method, the moment method, etc.
Among them, the moment method only has to set the boundary plane of an analysis target discrete in a 2-dimensional array, and is expected as a method more practical than the difference method and the finite element method which require setting at maximum 4-dimensional time space discrete. A reference document is xe2x80x98H. N. Wang, J. H. Richmond and M. C. Gilreath: Sinusoidal reaction formulation for radiation and scattering from conducting surface IEEE TRANSACTIONS ANTENNAS PROPAGATION vol. AP-23 1975xe2x80x99.
In these simulating methods, electric currents flowing through each element of an electronic appliance can be simulated by solving simultaneous linear equations defined in a frequency domain. Thus, when the simulation is performed in a time domain in the simulation method, it is necessary to solve simultaneous linear equations on a number of frequencies for the same target as analysis targets. In addition, when there is a wave source having a number of frequencies, it is also necessary to solve simultaneous linear equations on a number of frequencies for the same target as analysis targets.
To solve the simultaneous linear equations at a high speed, the FFS method (Fast Frequency Stepping method) has been used in some cases as described by xe2x80x98G. Hoyler, R. Unbehauen, An Efficient Algorithm for The Treatment of Multiple Frequencies with The Method of Moments, Proceedings of EMCxe2x80x99 96 ROMA pp. 368-371 (1996). In the FFS method, simultaneous linear equations are first derived using the lowest frequency as an analysis target. Then, the Cholesky factorization (A=CCt) is performed on the coefficient matrix of the simultaneous linear equations, and the simultaneous linear equations are solved in the direct method. Then, an analytic frequency is selected in the ascending order of frequencies, and simultaneous linear equations are derived using the analytic frequency as an analysis target. Then, the simultaneous linear equations are solved in the iterative method using a preconditioned matrix (C) obtained in the first direct method. This is the FFS method.
Described below is a numeric solution of simultaneous linear equations. A method of solving the simultaneous linear equations xe2x80x98Ax=bxe2x80x99 (coefficient matrix A=(aij) is a complex symmetric matrix) as shown in FIG. 1 can be the direct method or the iterative method.
The direct method can be followed by performing the Cholesky factorization on the coefficient matrix A (LU factorization on a symmetric matrix) as shown in FIG. 2, and a solution (xi) is obtained by the equation shown in FIG. 3. The number of required computations is the order of O(n3)(n is the degree of the coefficient matrix A).
On the other hand, the iterative method referred to as a conjugate gradient method is described below. In the iterative method, a solution (xi) is obtained by obtaining the value xe2x80x98x(k+1)xe2x80x99 at the (k+1)th stage using the values xe2x80x98x(k), xcex1(k), p(k)xe2x80x99 at the k-th stage according to the algorithm shown in FIG. 4. The number of required computations is the order of O(Kn2)(n is the degree of the coefficient matrix A, and K is the number occurrences having the maximum value of n). Therefore, it has the advantage over the direct method in quantity of computations.
In the iterative method, when the coefficient matrix A is A≈CCxcfx84, which is close to the Cholesky factorization, the original simultaneous linear equations xe2x80x98Ax=bxe2x80x99 are transformed as follows.
Cxe2x88x921ACt*xe2x88x921Ctx=Cxe2x88x921b
where Cxe2x88x921 is an inverse matrix of the matrix C,
Ct is a transposed matrix of the matrix C, and
Ct*xe2x88x921 is an inverse matrix of the transposed matrix of the matrix C.
At this time, the matrix Cxe2x88x921ACt*xe2x88x921 is very close to a unit matrix, and is expected to quickly converge. This is referred to as a preconditioned conjugate gradient method, and is performed by the algorithm shown in FIG. 5.
When simultaneous linear equations are solved on a number of frequencies for the same target as analysis targets using the above described algorithms in the conventional methods, an FFS method has been used in which simultaneous linear equations are first derived using the lowest frequency as an analysis target, and the coefficient matrix of the simultaneous linear equations is processed in the Cholesky factorization (A=CCt), the simultaneous linear equations are solved in the direct method, then the analytic frequency is selected in the ascending order of frequencies, simultaneous linear equations are derived using the analytic frequency as an analysis target, and the simultaneous linear equations are solved in the iterative method using the preconditioned matrix (C).
However, according to the above described conventional technology, as the analytic frequency selected in the ascending order becomes farther from the lowest frequency, the preconditioned matrix deviates from a desired mode. As a result, the analysis time in the iterative method is prolonged, thereby arising the problem that a high-speed simulating process cannot be performed.
That is, as the analytic frequency selected in the ascending order becomes farther from the lowest frequency, the matrix Cxe2x88x921ACt*xe2x88x921 deviates from a unit matrix. As a result, the analysis time in the iterative method is prolonged, thereby arising the problem that a high-speed simulating process cannot be performed.
The present invention has been developed based on the above described background, and aims at providing a new simulating apparatus and method for quickly realizing a simulating process when an electric current flowing through electronic appliances is simulated by solving simultaneous linear equations defined depending on an analytic frequency in the moment method, etc., and at providing a new program storage medium storing a program for realizing the simulation apparatus.
The present invention is based on an apparatus and a method for simulating an electric current flowing through electronic appliances by solving simultaneous linear equations defined depending on an analytic frequency, or a computer-readable storage medium storing a program for directing a computer to perform the simulation.
According to the first embodiment of the present invention, the following configuration is designed.
First, an analytic frequency is selected from the frequency area to which the analytic frequency belongs excluding the frequencies at both ends of the analytic frequency area.
Then, the simultaneous linear equations defined depending on the selected analytic frequency are solved in the direct method.
Then, the analytic frequencies after the selected analytic frequency are sequentially selected, and the simultaneous linear equations defined by the selected analytic frequency are solved in the iterative method.
With the above described configuration, the frequency distance (frequency difference) between the analytic frequency in which simultaneous linear equations are solved in the iterative method and the frequency in which they are solved in the direct method can be shorter than in the conventional technology. That is, the simultaneous linear equations solved in the iterative method can be transformed into a form in which they can be converged into a solution.
According to the second embodiment of the present invention, the following configuration can be designed.
First, an area to which an analytic frequency belongs is divided into a plurality of areas.
Then, one analytic frequency is selected from each of the divided analytic frequency areas.
Next, the simultaneous linear equations defined depending on the selected analytic frequency are solved in the direct method.
Then, the subsequent analytic frequencies are selected from each of the divided analytic frequency areas, and the simultaneous linear equations defined by the selected analytic frequency are solved in the iterative method.
With the above described configuration, the frequency distance between the analytic frequency in which simultaneous linear equations are solved in the iterative method and the frequency in which they are solved in the direct method can be shorter than in the conventional technology. That is, the simultaneous linear equations solved in the iterative method can be transformed into a form in which they can be converged into a solution.
According to the third embodiment of the present invention, the following configuration can be designed.
First, the first analysis is performed by solving the simultaneous linear equations defined depending on the specified analytic frequency in the direct method.
Then, the second analysis is performed by sequentially selecting the analytic frequencies after the selected analytic frequency, and solving the simultaneous linear equations defined by the selected analytic frequency in the iterative method.
Then, it is determined which is an advantageous method for solving simultaneous linear equations by the second analysis, in the direct method or in the iterative method. If it is determined that the direct method is advantageous, then the first analysis is performed on the simultaneous linear equations.
With the above described configuration, if the analysis time is prolonged by solving the simultaneous linear equations in the iterative method, then the direct method is performed, and the subsequent analysis is performed such that the simultaneous linear equations can be solved in the iterative method using the analysis result. Thus, the simultaneous linear equations solved in the iterative method can be transformed into a form in which they can be converged into a solution at a higher speed.
As described above, a simulating process can be realized at a high speed when a configuration for simulating an electric current flowing through electronic appliances is designed by solving the simultaneous linear equations defined depending on the analytic frequency in the moment method, etc. according to any embodiment of the present invention.